A fuel injector for injecting fuel into a combustion engine typically comprises a valve that can be opened by means of an electrically driven actuator. Different designs for such fuel injection valves are known in the art. Many known designs suffer from poor vaporization of the fluid dispensed through the injection hole and/or imprecise dosing of the fluid, e.g., due to an insufficiently fast closing caused by an inadequate hydraulic force on the valve needle in the closing direction.